EXPONENTIAL MIXING OF CONSTRAINED RANDOM DYNAMICAL SYSTEMS VIA CONTROLLABILITY CONDITIONS

被引：0

作者：

Mertz, Laurent ^{[1
]}

Nersesyan, Vahagn ^{[2
]}

Rissel, Manuel ^{[2
]}

机构：

[1] City Univ Hong Kong, Dept Math, Kowloon, Hong Kong, Peoples R China

[2] NYU Shanghai, NYU ECNU Inst Math Sci, 3663 Zhongshan Rd North, Shanghai 200062, Peoples R China

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2024年 / 62卷 / 06期

关键词：

differential inclusions; elasto-plasticity; ergodicity; exponential mixing; controllability; white noise; decomposable noise; ELASTOPLASTIC PROBLEM; PLASTIC-DEFORMATION;

D O I：

10.1137/24M164999X

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We provide deterministic controllability conditions that imply exponential mixing properties for randomly forced constrained dynamical systems with possibly unbounded state space. As an application, new ergodicity results are obtained for nonsmooth models in elasto-plasticity driven by various types of noise, including white noise. It is thereby illustrated how tools from control theory can be utilized to tackle regularity issues that commonly arise in the qualitative study of constrained systems.

引用

页码：3266 / 3287

页数：22

共 26 条

[1] On finite-dimensional projections of distributions for solutions of randomly forced 2D Navier-Stokes equations [J].

Agrachev, A. ;

Kuksin, S. ;

Sarychev, A. ;

Shirikyan, A. .

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2007, 43 (04) :399-415

[2] Navier-Stokes equations: Controllability by means of low modes forcing [J].

Agrachev, AA ;

Sarychev, AV .

JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2005, 7 (01) :108-152

[3]

Arnold L., 1987, Stochastics, V21, P41, DOI 10.1080/17442508708833450

[4] Degenerate dirichlet problems related to the invariant measure of elasto-plastic oscillators [J].

Bensoussan, Alain ;

Turi, Janos .

APPLIED MATHEMATICS AND OPTIMIZATION, 2008, 58 (01) :1-27

[5] Stochastic variational inequalities for elasto-plastic oscillators [J].

Bensoussan, Alain ;

Turi, Janos .

COMPTES RENDUS MATHEMATIQUE, 2006, 343 (06) :399-406

[6] Long cycle behavior of the plastic deformation of an elasto-perfectly-plastic oscillator with noise [J].

Bensoussan, Alain ;

Mertz, Laurent ;

Yam, S. C. P. .

COMPTES RENDUS MATHEMATIQUE, 2012, 350 (17-18) :853-859

[7] An analytic approach to the ergodic theory of a stochastic variational inequality [J].

Bensoussan, Alain ;

Mertz, Laurent .

COMPTES RENDUS MATHEMATIQUE, 2012, 350 (7-8) :365-370

[8] AN ULTRA WEAK FINITE ELEMENT METHOD AS AN ALTERNATIVE TO A MONTE CARLO METHOD FOR AN ELASTO-PLASTIC PROBLEM WITH NOISE [J].

Bensoussan, Alain ;

Mertz, Laurent ;

Pironneau, Olivier ;

Turi, Janos .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2009, 47 (05) :3374-3396

[9]

Bensoussan Alain., 2010, Applied and Numerical Partial Differential Equations, P9, DOI [10.1007/978-90-481-3239-33, DOI 10.1007/978-90-481-3239-33]

[10]

Bogachev V.I., 1998, Gaussian Measures

← 1 2 3 →